Code
import matplotlib.pyplot as plt
import networkx as nx
import pandas as pdImportant nodes - Network analysis
python
datacamp
network analysis
machine learning
NetworkX
Important nodes - Network analysis
This course will introduce us to the advanced concepts of network analysis and the basics of path finding algorithms while identifying nodes that are important in a network. This chapter concludes with a look at the Twitter network dataset, which will reinforce concepts such as degree centrality and betweenness centrality that you have learned.
This Important nodes is part of Datacamp course: Introduction to Network Analysis in Python
This is my learning experience of data science through DataCamp. These repository contributions are part of my learning journey through my graduate program masters of applied data sciences (MADS) at University Of Michigan, DeepLearning.AI, Coursera & DataCamp. You can find my similar articles & more stories at my medium & LinkedIn profile. I am available at kaggle & github blogs & github repos. Thank you for your motivation, support & valuable feedback.
These include projects, coursework & notebook which I learned through my data science journey. They are created for reproducible & future reference purpose only. All source code, slides or screenshot are intellactual property of respective content authors. If you find these contents beneficial, kindly consider learning subscription from DeepLearning.AI Subscription, Coursera, DataCamp
Code
T = pd.read_pickle('dataset/ego-twitter.p')Degree centrality
Compute number of neighbors for each node
How do you evaluate whether a node is an important one or not? There are a few ways to do so, and here, you’re going to look at one metric: the number of neighbors that a node has.
Your job in this exercise is to write a function that returns all nodes that have m neighbors.
Code
T.neighbors(19)<dict_keyiterator at 0x141e1d4f0>Code
list(T.neighbors(19))[5,
8,
12035,
5399,
11,
5380,
13,
15,
4390,
17,
5411,
20,
21,
24,
5426,
12036,
12037,
30,
12038,
5437,
5439,
31,
35,
36,
37,
5485,
48]Code
# Define nodes_with_m_nbrs()
def nodes_with_m_nbrs(G, m):
"""
Returns all nodes in graph G that have m neighbors.
"""
nodes = set()
# Iterate over all nodes in G
for n in G.nodes():
# Check if the number of neighbors of n matches m
if len(list(G.neighbors(n))) == m:
# Add the node n to the set
nodes.add(n)
# Return the nodes with m neighbors
return nodes
# Compute and print all nodes in T that have 6 neighbors
six_nbrs = nodes_with_m_nbrs(T, 6)
print(six_nbrs){22533, 1803, 11276, 11279, 6161, 4261, 10149, 3880, 16681, 5420, 14898, 64, 14539, 6862, 20430, 9689, 475, 1374, 6112, 9186, 17762, 14956, 2927, 11764, 4725}Great work! The number of neighbors a node has is one way to identify important nodes. It looks like 25 nodes in graph T have 6 neighbors.
Compute degree distribution
The number of neighbors that a node has is called its “degree”, and it’s possible to compute the degree distribution across the entire graph. In this exercise, your job is to compute the degree distribution across T.
Code
# Compute the degree of every node: degrees
degrees = [len(list(T.neighbors(n))) for n in T.nodes()]
# Print the degrees
print(degrees)[47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 10, 27, 0, 0, 0, 0, 0, 0, 0, 0, 34, 0, 0, 0, 0, 0, 60, 0, 11, 4, 0, 12, 0, 0, 56, 53, 0, 30, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 6, 0, 0, 0, 0, 0, 33, 0, 0, 0, 0, 39, 8, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 26, 0, 5, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 7, 0, 0, 0, 0, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 95, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]Degree centrality distribution
The degree of a node is the number of neighbors that it has. The degree centrality is the number of neighbors divided by all possible neighbors that it could have. Depending on whether self-loops are allowed, the set of possible neighbors a node could have could also include the node itself.
Code
# Compute the degree centrality of the Twitter network: deg_cent
deg_cent = nx.degree_centrality(T)
# Plot a histogram of the degree centrality distribution of the graph.
plt.figure()
plt.hist(list(deg_cent.values()))
plt.xlabel('centrality')
plt.ylabel('count')
plt.show()
# Plot a histogram of the degree distribution of the graph
plt.figure()
plt.hist(degrees)
plt.xlabel('neighbors')
plt.ylabel('count')
plt.show()
# Plot a scatter plot of the centrality distribution and the degree distribution
plt.figure()
plt.scatter(degrees, list(deg_cent.values()))
plt.xlabel('degrees')
plt.ylabel('centrality')
plt.show()
Graph algorithm
Shortest Path
You can leverage what you know about finding neighbors to try finding paths in a network. One algorithm for path-finding between two nodes is the “breadth-first search” (BFS) algorithm. In a BFS algorithm, you start from a particular node and iteratively search through its neighbors and neighbors’ neighbors until you find the destination node.
Code
# Define path_exists()
def path_exists(G, node1, node2):
"""
This function checks whether a path exists between two nodes (node1, node2) in graph G.
"""
visited_nodes = set()
# Initialize the queue of nodes to visit with the first node: queue
queue = [node1]
# Iterate over the nodes in the queue
for node in queue:
# Get neighbors of the node
neighbors = G.neighbors(node)
# Check to see if the destination node is in the set of neighbors
if node2 in neighbors:
print('Path exists between nodes {0} and {1}'.format(node1, node2))
return True
breakShortest Path II
Now that you’ve got the code for checking whether the destination node is present in neighbors, next up, you’re going to extend the same function to write the code for the condition where the destination node is not present in the neighbors.
Code
def path_exists(G, node1, node2):
"""
This function checks whether a path exists between two nodes (node1, node2) in graph G.
"""
visited_nodes = set()
queue = [node1]
for node in queue:
neighbors = G.neighbors(node)
if node2 in neighbors:
print('Path exists between nodes {0} and {1}'.format(node1, node2))
return True
else:
# Add current node to visited nodes
visited_nodes.add(node)
# Add neighbors of current node that have not yet been visited
queue.extend([n for n in neighbors if n not in visited_nodes])Shortest Path
Code
def path_exists(G, node1, node2):
"""
This function checks whether a path exists between two nodes (node1, node2) in graph G.
"""
visited_nodes = set()
queue = [node1]
for node in queue:
neighbors = G.neighbors(node)
if node2 in neighbors:
print('Path exists between nodes {0} and {1}'.format(node1, node2))
return True
break
else:
visited_nodes.add(node)
queue.extend([n for n in neighbors if n not in visited_nodes])
# Check to see if the final element of the queue has been reached
if node == queue[-1]:
print('Path does not exist between nodes {0} and {1}'.format(node1, node2))
# Place the appropriate return statement
return FalseBetweenness centrality
NetworkX betweenness centrality on a social network
Betweenness centrality is a node importance metric that uses information about the shortest paths in a network. It is defined as the fraction of all possible shortest paths between any pair of nodes that pass through the node.
Code
# Compute the betweenness centrality of T: bet_cen
bet_cen = nx.betweenness_centrality(T)
# Compute the degree centrality of T: deg_cen
deg_cen = nx.degree_centrality(T)
# Create a scatter plot of betweenness centrality and degree centrality
plt.scatter(list(bet_cen.values()), list(deg_cen.values()))
plt.xlabel('betweenness_centrality')
plt.ylabel('degree_centrality')
# Display the plot
plt.show()
Code
# Define find_nodes_with_highest_deg_cent()
def find_nodes_with_highest_deg_cent(G):
# Compute the degree centrality of G: deg_cent
deg_cent = nx.degree_centrality(G)
# Compute the maximum degree centrality: max_dc
max_dc = max(list(deg_cent.values()))
nodes = set()
# Iterate over the degree centrality dictionary
for k, v in deg_cent.items():
# Check if the current value has the maximum degree centrality
if v == max_dc:
# Add the current node to the set of nodes
nodes.add(k)
return nodesCode
# Find the node(s) that has the highest degree centrality in T: top_dc
top_dc = find_nodes_with_highest_deg_cent(T)
print(top_dc)
# {11824}
# Write the assertion statement
for node in top_dc:
assert nx.degree_centrality(T)[node] == max(nx.degree_centrality(T).values()){11824}It looks like node 11824 has the highest degree centrality.
Deep dive – Twitter network part II
Next, you’re going to do an analogous deep dive on betweenness centrality!
Code
# Define find_node_with_highest_bet_cent()
def find_node_with_highest_bet_cent(G):
# Compute betweenness centrality: bet_cent
bet_cent = nx.betweenness_centrality(G)
# Compute maximum betweenness centrality: max_bc
max_bc = max(list(bet_cent.values()))
nodes = set()
# Iterate over the betweenness centrality dictionary
for k, v in bet_cent.items():
# Check if the current value has the maximum betweenness centrality
if v == max_bc:
# Add the current node to the set of nodes
nodes.add(k)
return nodesCode
# Use that function to find the node(s) that has the highest betweenness centrality in the network: top_bc
top_bc = find_node_with_highest_bet_cent(T)
print(top_bc)
# {1}
# Write an assertion statement that checks that the node(s) is/are correctly identified.
for node in top_bc:
assert nx.betweenness_centrality(T)[node] == max(nx.betweenness_centrality(T).values()){1368}KeyboardInterrupt: You have correctly identified that node 1 has the highest betweenness centrality!